let p, q be Element of CQC-WFF ; :: thesis: for h being QC-formula
for x, y being bound_QC-variable st p = h . x & q = h . y & not x in still_not-bound_in q & not y in still_not-bound_in h holds
(Ex x,p) => (Ex y,q) is valid
let h be QC-formula; :: thesis: for x, y being bound_QC-variable st p = h . x & q = h . y & not x in still_not-bound_in q & not y in still_not-bound_in h holds
(Ex x,p) => (Ex y,q) is valid
let x, y be bound_QC-variable; :: thesis: ( p = h . x & q = h . y & not x in still_not-bound_in q & not y in still_not-bound_in h implies (Ex x,p) => (Ex y,q) is valid )
assume that
A1: ( p = h . x & q = h . y ) and
A2: not x in still_not-bound_in q and
A3: not y in still_not-bound_in h ; :: thesis: (Ex x,p) => (Ex y,q) is valid
A4: not x in still_not-bound_in (Ex y,q) by A2, Th6;
p => (Ex y,q) is valid by A1, A3, Th25;
hence (Ex x,p) => (Ex y,q) is valid by A4, Th22; :: thesis: verum